Subfields of the function field of the deligne-Lusztig curve of ree type

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2002
Çakçak, Emrah
Let X be the Deligne-Luzstig curve of Ree type defined over ¥q,q = 32s+1, s > 1 and F its function field. One of the main problem here is to construct a large number of nonrational subfields of F and compute their genera. For this, we consider the fixed fields FH, of F, under subgroups H of G, where G = Aut(F/F9) is the automor phism group of F/Fg. In this thesis, we show how one can compute the genera of FH for various subgroups H of G. Our computation here is based on the facts that: G is a Ree group which acts as a permutation group on the set of rational places of F and this action of G is nothing but the usual 2-transitive representation of the Ree group.

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Citation Formats
E. Çakçak, “Subfields of the function field of the deligne-Lusztig curve of ree type,” Ph.D. - Doctoral Program, Middle East Technical University, 2002.